Step by step
The question
Question: solve 3m + 8 = 5m − 2.
1 Get m on one side
There is m on both sides.
We want m on one side only.
So we remove the 3m from the left side.
To remove 3m, we take away 3m.
We do it on both sides.
Why both sides?
The = sign means both sides are the same amount.
If we change only one side, they are not the same any more.
3m and − 3m make zero.
Cross them out.
5m − 3m = 2m.
Now we have 8 = 2m − 2.
Let's swap the two sides, so m is on the left.
We want m by itself.
Two things are stuck to m: times 2 and − 2.
The − 2 is on the outside, so it comes off first.
Then the times 2.
2 Remove the − 2
To remove − 2, we add 2.
We do it on both sides, so they stay equal.
− 2 and + 2 make zero.
Cross them out.
8 + 2 = 10.
Now we have 2m = 10.
3 Remove the 2
2m means 2 times m.
We want just m.
To remove times 2, we divide by 2.
We do it on both sides, so they stay equal.
2 divided by 2 is 1.
So just m is left.
10 divided by 2 is 5.
So m = 5!
4 Check
Let's check: put 5 in place of m.
First the left side.
Now the right side.
Both sides are 23.
So m = 5 is right!
Let's look back.
First: get m on one side.
Then: remove the − 2.
Then: remove the 2.
Last: check.